Final answer:
The variance of the set cannot be directly computed from ordered pairs, and assuming the dataset consists of first elements of each pair, the actual variance is 1.7, which is not among the provided options. There seems to be an error in the question.
Step-by-step explanation:
To find the variance of the set {(1, 1), (2, 4), (3, 3), (4, 5), (4, 4)}, we first need to understand that the question seems to be improperly formatted, as the given set contains ordered pairs which are typical for coordinates, not individual numbers from which a variance can be directly computed. Assuming this is an error and the dataset for which we need to compute the variance is actually the first elements of these pairs (or the second elements, the method will be the same), we would proceed as follows:
- Calculate the sample mean (average) of the dataset.
- Subtract the mean from each data point to find the deviation of each point.
- Square each deviation to find the squared deviations.
- Compute the average of these squared deviations; this is the variance.
Following these steps, consider the dataset composed of the first elements of each pair: (1, 2, 3, 4, 4). The mean of this dataset is (1+2+3+4+4) / 5 = 14 / 5 = 2.8. Now, we find the deviations: (1-2.8)^2, (2-2.8)^2, (3-2.8)^2, (4-2.8)^2, and (4-2.8)^2. These squared deviations are 3.24, 0.64, 0.04, 1.44, and 1.44. The sum of these is 6.8. To find the variance, we divide by the number of observations minus 1 (which is 4 in this case because we're dealing with a sample, not a population): variance = 6.8 / 4 = 1.7.
The correct variance is not provided among the options. Hence, a clarification of the data set to be considered for the calculation would be necessary, or there may have been a mistake in the provided options.